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Variation of parameters - i have different particular soluti

  1. Jan 25, 2016 #1
    i was trying to get a particular solution of a 3rd order ODE using the variation of parameters method
    the homogeneous solution is yh = c1 e-x + c2 ex + c3 e2x
    the particular solution is yp=y1u1+y2u2+y3u3
    as u1=∫ (w1 g(x) /w) dx , u2=∫ (w2 g(x) /w) dx , u3=∫ (w3 g(x) /w) dx
    w =
    |y1 y2 y3|
    |y'1 y'2 y'3|
    |y''1 y''2 y''3|

    when i choose y1 , y2 , y3 to be e-x,ex,e2x i get an answer ,
    but when i change the arrangement (like: ex,e-x,e2x )
    i get another different answer !

    so , i have two questions
    1 is it normal to have different results when changing who is y1 , y2 , y3 , or am i doing something wrong?
    2 if it is normal , does that mean i can have too many different particular solutions , just by changing who is y1 , y2 , y3?
  2. jcsd
  3. Jan 25, 2016 #2


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    2017 Award

    Staff: Mentor

    What are the different answers you get?
    Maybe they are equivalent, and just look differently?
  4. Jan 25, 2016 #3
    ummmmmm .... ahhhh .. actually ... when you asked me to show the results i went to prepare them for uploading
    and as i was rewriting the solution i discovered an extra (2) multiplied in one little tiny term , will i fixed it and went on , and the results were the same indeed , i am terribly sorry for this mistake it happened because i trusted the solution of a senior without a thorough revision
    thank you for your reply :smile: and i apologies again.
  5. Jan 28, 2016 #4


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    Science Advisor

    Never trust a senior!
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